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arXiv:quant-ph/0606176 · Journal of Physics A Mathematical and Theoretical

On non-completely positive quantum dynamical maps on spin chains

W. A. Majewski

Published Sep 4, 2007• 11 citations
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Abstract

The new arguments based on the Majorana fermions model indicating that non-completely positive maps can describe open quantum evolution are presented.
DOI
10.1088/1751-8113/40/38/006

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In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation.